One of the most significant advances during the past year was the development of theoretical principles which allow optimization of adiabatic pulses for broadband excitation (i.e., pulses that can perform uniform rotations despite extreme variations of frequency offset, W). An analytical expression was derived which describes the necessary relationship between the amplitude- and frequency-modulated functions of the adiabatic pulses. All pulses predicted from this equation require an equivalent amount of average radiofrequency power, and this power level corresponds to the minimum possible to achieve excitation uniformly across any given bandwidth. In simulations of adiabatic inversion, our new pulses perform better than previous adiabatic pulses (such as the popular hyperbolic secant pulse (Tsekos et al. 1995b)), as judged from the sharpness of the transition regions at the edges of the frequency response profiles. In addition, our new theory allows adiabatic pulses to be optimally tailored to meet power limitations in different NMR experiments. The power (and specific absorption rate (SAR)) required for broadband inversion, refocusing, and decoupling can be substantially reduced with these new pulses.